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Welcome to fourth lecture of video course on Tribology. We are going to discuss on how
to estimate friction with reliability, providing results as we get from experiments. In previous
lecture we discussed three theories; adhesion, then plowing by conical theory and plowing
by spherical asperity theory.
If we summarise those three theories what we get; in adhesion generally two surfaces
get valid under pressure. That is why we call they these mode of friction as adhesion friction.
In second and third it is a displacement of surface, displacement of material due to the
asperities of hard material. And we develop mathematical relations for adhesion we say
it is a ratio of shear strength to the hardness. Lower the shear the strength of material higher
the higher hardness will provide lower coefficient of friction.
However, we discussed also what are the drawbacks that are mentioned that if same material has
been used against a number of spheres this theory will provide same coefficient of friction
for all material sphere which is not right. Then, we develop mathematical relation for
friction by deformation or we say the conical asperity deformation deformation caused by
conical asperity and we developed the relation as a 2 by pi into cot theta. It is a very
sensitive relation and here the theta is a half angle half cone. If I simplify say the
two divide by pi is equal to 0.063666 are the nearby 0.64 and express in terms of death
or penetration and radius of the cone at interphone then I will get relation something like that
0.64 in to h divide by r. This is more or less same relation which we developed for
spherical asperities. The same way mu d for spherical asperity was a 0.6 square root of
h by r; r is a radius of spherical asperity. So, there is a lot of symmetry between the
second relation and third relation. Only thing is that, in second it is much more sensitive
effect of h is much more dominant compared to effect which is shown in expression third
deformation by asperity, a spherical asperity. In totality, all these three expressions are
not providing very good results. That is why the and Drabber who developed theory based
on adhesion initially tried to modify it assuming that possible there is a possibility of this
area to be extended or grow as we apply tangential force and other were friction force is going
to increase area of contact. That was their hypothesis.
And then they tried to give some explanation, some derivation or mathematical derivation.
To elaborate I am just taking these two spheres enouncing assuming both the spheres are of
rough they come into contact only at the asperities. We can see there is a area of contact some
force is been applied the normal force is been applied, some tangential force is been
applied force equilibrium is shown in this element.
If I take a help of principle stresses or use a solid mechanics to drive the relation;
what we can get principle stress one principal stress two is equal to average stress, stress
in x direction and x stress in y direction plus minus plus will be for sigma one and
minus will be for sigma two. Then this is the average plus there is a shear strength.
If I simplify it we say that assume there is a normal load only in y direction and x
direction there is no force then, sigma x will be zero sigma y will be the normal force
divided by area or projected area while shear stress will be friction force divided by contact
area. These are the simple expression. Difficult expression can be achieved, but, we want to
find out initially or this is approximate relation which can give some results close
to the experiment results.
Now, if I use a expression sigma one with a plus sign and sigma two with a minus sign,
I will be getting relations something like this and we know very well if we subtract
expression two from expression one; I will be getting the difference in principle stress
and that should be the minimum yield strength of the material which is supporting that kind
of load or supporting the w load. So, you subtract and we get expression something like
this you can see there is a normal force divided by two plus tangential force and this is sigma
one minus sigma two which I am saying that this should be equal to a minimum value of
yield strength should be equal to this. It can be more than that, but, minimum value
should be like this.
We can substitute those values sigma y is equal to sigma one minus sigma two and if
I use a shear strength approximation we say that shear strength is generally fifty percent
of yield strength. Depend on the which theory I am using or which component maximum shear
stress or Tresca theory I am using. If the Tresca theory then this is will be the .577
sigma y while one might say that will be .75 .7577. While in case of Tresca theory it will
be 50 percent of yield strength. We substitute these values what we get expressions
something like this as the area or elemental area into shear strength of material, expression
for normal force or is fifty percent of normal force is square of that and then tangential
force. For present case we are assuming the normal load is not going to change. It remains
same. Material sphere is not going to change it remains same. What is the meaning of that
this w and tau y is not going to change. So, this indicates if we increase value of f,
value of a need to be increased to give reliable results or we can say friction force is a
function of area of contact. Friction force is function of area of contact. With increase
in a friction force area of contact will continuously increase. But, there will be a limiting value.
Beyond certain area it cannot be increased further. If we can say the limiting value
of e is equal to a max right. So, it will reach to one level and to differentiate
between the shear strengths we can say that, lets take a shear strength of a interphase
and represent as a tau I where friction force or we say one surface will be getting separated
from other surface. There will be a breakage of contact or breakage of cool welds which
were made during the normal load or initial load. Then only the sliding will start. We
can we can represent f as a tau I, shear strength of interphase into area of that is a limiting
area a max. If we substitute those values what we get? Half limiting or our friction
force is equal to tau I into area maximum area which can be developed, which can be
grown to the maximum value.
And if I substitute these values in this expression which we derived in previous slide what we
gave something like this; a max into tau y square the area is continuously increasingly,
this normal force will remain same or term which contain the normal force will be the
same. And last expression is a friction force. We can rearrange, we can find out the value
of w from this what will be the maximum value which we can be applying or it can be applied
on this interphase. And we know coefficient of friction can be represented as a friction
force divided by normal load. I can substitute this tau I into a max over here and w after
rearranging can be represented in this form, two square root of tau square tau y square
minus tau I square in bracket and multiply with a max square. a max and this a max will
cancel out and what we will get the expression in terms of shear strengths. Shear strength
of the interphase shear strength of soft material that is the difference. We are saying that
there is a difference. If interphase is getting fractured at the
value of shear strength of material then coefficient of friction will be very very high. However,
if the shear strength of the interphase is very low, irrespective of what is the value
of the tau I the coefficient of friction will be lesser and this is the reason why we provide
lubricant. If we provide lubricant at the interphase shear strength of interphase will
be almost negligible compared to the solid material strength. Just to get a feel of that
we did some calculations. We say let us take a example the tau tau I by tau y this can
be given in a some ratio. Let us take a tau y tau I divided by tau y
is one percent or .01. If with that is the case, if interfacial strength is just one
percent of soft material shear strength, coefficient of friction is almost negligible. It is a
.005. If we increase that to the ten percent, we say interphase is made in such a manner,
interfacial strength is ten percent of soft material shear strength and coefficient of
friction increases also ten times. Earlier it was .005, now here it is a .05. We further
increase to 20 percent what we get? It is almost double from 10 to 20 is almost getting
double from .05 to the .1. Similarly, we can do more number of iterations
and we come to the result. See when is a ninety nine percent, interfacial strength is a ninety
nine percent of the bulk shear strength of soft material coefficient of friction is predicted
as a 3.5 and this is very close to the what we got the result from experiments. Experimental
result shows that they are two soft materials are used. Their interphase shear strength
will be very high almost equal to the one of the weak material shear strength and coefficient
of friction can be very high may be say 3 to 4 or 3.5 what we are getting from here
right. So, we can interpret our result, the stabile
result in such a manner the ratio of shear strengths decide mu. It is not a absolute
value of tau I or tau y. Decide the what will be the, what will be the coefficient of friction
or what will be coefficient of friction due to adhesion. But, it is a ratio which decides
if its strength interphase is strong and bulk material is also strong then, we will get
a one kind of shear strength. If the interphase is weak; weak in the sense it having a cold
junction, form cold junction then, again the shear strength of the material will be comparable
to interphase again. The coefficient of friction will be very high.
However, if I say in terms of strong interphase, strong in the terms it is related to material
and it is attached firmly to the material or one layer which is firmly attached to the
parent material in that case, there is a possibility of low interfacial shear strength. To elaborate
that lets take one picture and see this is one of the soft, one of the material metal
surface which has a work harden surface then oxide layer due to availability of oxygen
and environment and some absorption, some contamination. And these layers are a very
very thin. We are talking about the thirty Armstrong, that 100 Armstrong and in this
case may be roughly ten micron. So, when the material is a ***, behaviour
of the material will be different. If it is a work harden, if we say ten micron work hardening
layer on that then its interfacial strength will change or interaction with other material
will change. In that next one is that oxide layer if there is oxide layer may be say even
hundred Armstrong, that can change the interfacial strength. In short these layer decide the
behaviour of tribe surfaces. If all three layers, all four layers are removed from the
surface then we will be getting very high coefficient of friction and in fact, it happens
in the soft materials like a gold, indium they do not get the those many layers. However,
in the steel chromium we can get a good number of layers, good, excite layers on the top
of the surface and they prevent adhesion they make interphase, weak shear strength surface
or shear strength of interphase is almost negligible in those cases. That is why we
get a low coefficient of friction. However, if we remove these layers coefficient
of friction will increase. We can do this kind of experiment in the laboratory when
the shaft is machined and if we immediately we try to run at the high speed, we will find
there is a high coefficient of friction and complete welding on that. However, if we grease
it and then run in bearing or a soft surface we will find coefficient of friction is much
lesser. Reason being the lubricant layer or this layer has a thin or coat of thin layer
on the shaft surface and reduce the interphase shear strength, that interphase shear strength
compared to the bulk shear strength of a steel shaft and then we will get a good result.
And in this case, feasibly that if the surface roughness of the other surface may be say
they are two surfaces and one surface has a coating this kind of layers and other surface
has a high hardness with high surface roughness. This may damage the protective layer; that
means, if surface roughness is very high there is a possibility of damaging those protective
layers and increasing the coefficient of friction in those cases. We somehow do not want that
kind of thing that is why we are always preferring low shear low surface roughness of the surface
as well as some protective layer. In short adhesion theory which was tried using the
junction growth is applicable along with asperity contact where the asperities need to be much
lesser in size in height as well as in hardness. So, that they do not create cavities or ploughing
effect on the soft surface.
I can think over some possible situations; we say that assume the metal is weak and oxide
layer is weak. Here when we are talking about the weak oxide it is not in obsolesce, it
is only relative sense. This layer attached with ductile material and strength of that
layer over ductile material is low we are not talking any other thing that. This is
the only attachment or adhesion to the parent material to the this ductile material is weak;
that means, it will be simply removed or abutted or delaminated if there is a some surface
roughness or some tangential force on applied by some harder surface.
So, what we are able to say in from that, the this film which is made as a weak oxide
film it can be easily broken because in bonding to the parent material is much weaker and
this kind of material with oxide weak oxide layer will undergo rapid junction growth.
Result very high value of mu, high coefficient of friction. Couple of example on which belong
to this category are indium, gold. Gold to gold we found a coefficient of friction very
high. Indium to indium we found the coefficient of friction very high. Even if the indium
versus gold will be having high coefficient of friction.
We can take another example we assume that there is a weak metal the shear strength is
low. But, there is a strong oxide here a strong oxide is adhesion of oxide layer on the material
exclusively that in that case what will happen initially there will be coefficient of friction
will be very low or we say reasonably low value. After sometime if the interphase or
rupture, interphase between the weak metal and oxide layer; we are not talking tribe
sphere we are talking about the metal and oxide layer if that is rupture then there
will be transition and that due to this transition coefficient of friction will increase drastically.
Examples are in this case are the copper and iron, we have found many times oxide layer
on a iron and if it is a deform excessively it will be removed from the surface and coefficient
of friction will suddenly increase. What we known at termed that as a transition load.
The last which is a most most favourable is a strong metal and strong oxide both surfaces
surface as well as oxide layer are firmly attached. They have a strong bounding or oxide
layer has a strong bounding on metal. In that case what will happen irrespective of the
loads because the strength of that bond is very high, all the loads it can sustain. I
mean I say all the load in is there is a reasonable extent of region is not going to immediately
rupture under slightly higher load or moderate load.
Example in for this category are this steel and chromium where they make a strong bounding
with oxide layer or layer which is formed due to environment due to contamination that
is a strong or bounding of that oxide layer is strong. If I plot this on the diagram what
we say that this red colour line belongs to the first category that is a weak metal and
weak oxide. While coming to second one the weak metal and a strong oxide can be plotted
something like a blue line we say that there is a stationery or may be say initially cost
and coefficient of friction and then there is a rupture of the layer and then that is
why there is a sudden increase in coefficient of friction or finally, we say that the green
colour line which is most favourable, we accept this is having a combination strong metal
and strong oxide. That layer is always appreciated whenever we design any tribal sphere we should
aim for this kind of layer so, that we can get low coefficient of friction. However,
if we want high coefficient of friction then we can choose first case, but, in that case
wear rate will be also very high and then we need to provide appropriate action or appropriate
tools to get solution. Now, this is a note finally, coming when the
slide is a both junction growth and ploughing effects. Here why I use a word two and three?
Two and three; that means, ploughing is generally occurred due to the two body and three body.
When we are talking about two body is something asperities which are firmly attached to the
surfaces and one if asperities and asperities are in coming into contact. When we are talking
about the three body ploughing in that case we are assuming there are some debris at the
interphase and that is creating some sort of ploughing effect. Let us take an example
of the sand. If sand comes between the two soft materials then the sand particle will
start ploughing or start digging either material one and material two.
So, that that will causes some frictional losses. We are talking that that the ploughing
due to three body and when we are talking about only asperities the two body ploughing
effect. They play important role and depend on the situation; either of these mechanism
will play dominated role if there is no lubricant extra smooth surface, high high adhesion between
the material sphere or high cohesion between the similar layer. Then coefficient of friction
due to adhesion will be very very high and ploughing will be almost negligible
However if there is a partial lubricant adhesion component can be reduced to almost negligible
level. But, because of a surface roughness there will be some ploughing effect and if
there is a clear separation between two surfaces then the ploughing as well as adhesion will
be negligible and then that can be treated as a full film lubrication which is not a
topic in this category. We will be discussing that topic in later when we start film film
lubrication mechanism.
Now, how to reduce a junction growth? Note it down few points few suggestions, not necessary
everything will work in one situation, but, one of the suggestions will work to reduce
the junction growth. Say if you want to really reduce the junction growth, do not think about
the dry lubrication. Provide some sort of lubricant either powder lubrication, solid
lubrication, semi solid lubrication or liquid lubrication which reduces the interfacial
strength between two surfaces is fine, is something like when we play carom board. We
use a powder lubrication, we provide a powder form similar kind of action which has a loose
strength lower shear strength that will work on this.
And there is a possibility to choose appropriate material. We say that when you choose low
soft material as a third material that it may provide as a low shear strength and that
may work. That is why many a times we are using a molybdenum disulphide between the
two contacting surfaces which has a very low shear strength. We can sustain the, molybdenum
disulphide can sustain high compressive load, but, shear strength is negligible, shear planes
will simply move unless some load. So, that is appreciated.
Next suggestion is that never use a same metal or metal which have a similar kind of chemical
structure or they have a high molecular attraction. To explain this we can take example of copper
or copper, the coefficient of friction is 1.0. Reason being if they are not this particular
sphere are not oxidised and they are version materials they will come in a contact they
will form cold conjunction unless shear force the junction will grow and finally, a limiting
shear strength will come which is by and large equal to bulk material of copper or shear
strength of copper itself. Coming to the second spheres; aluminium with
the low carbon steel again in this case the both material of soft material and when they
make a junction that junction will grow under tangential load. Coefficient of fraction in
that case will turn out to be .8. However, silver and the low carbonate steel is some
good example here their shear strength their interfacial strength is relatively low and
that is why they give low coefficient of friction. Sometime we play with the ductility also.
So, we say, we use this low ductile material which can easily rupture. Apply it slight
force on that we can easily ruptured at the interphase and that will provide a low coefficient
of friction. However, there is a problem if that rupture happens to be very rapid or it
deteriorate the surface roughness then we should not use this kind of suggestion, we
should use some sort of lubricant or many a times we use water to lubricate the surfaces.
And there is some observation which we got at the lab is that coefficient of friction
is not necessary remain same throughout the time from the start of operation to the end
of operation. Of course, we have already explained in the previous lecture what is the kinetic
coefficient of friction and what is the dynamic and what is the static coefficient of friction.
However there is a slight change in the terminology. Many times in a write in a book you find steady
coefficient of friction. Steady coefficient of friction is equal to the kinetic coefficient
of friction. What is the meaning of that? At the start there will be some coefficient
of friction, but, that will change that will be different than steady coefficient of friction
or kinetic coefficient of friction. So, there is a slight change in terminologies, a slight
confusion in terminology. That is when we say steady coefficient of friction that is
in the start before running in time. When we see steady coefficient of friction;
that is a kinetic coefficient of friction. It is going to happen during the working life
of a component. Running in time we are not counting and remaining whatever the number
of hours which that tribe pair can sustain that will show a steady nature of coefficient
of friction. We are talking about that; however, there is a possibility of change in coefficient
of friction even under steady running condition. What we say that when we are bringing two
new surfaces, just fresh surfaces they will there will be higher ploughing effect at the
start and relatively low adhesion. If the surfaces are unpolished the surface where
having a super finish they are perfectly polished then possibilities will be high adhesion and
low ploughing effect. But, we are talking about the normal manufacturing surfaces which
have relatively high roughness. In that case ploughing effect will be very high initially
compared to the adhesion. And if this process continues there will be
some rupture some breakage of the asperities. Due to that there will be a reduction in ploughing
effect or coefficient of ploughing will decrease. But, this due to this there will be increase
in coefficient of friction. Due to adhesion yeah more and more asperities are keep coming
in contact due to rupture or we say that rupture of high level or high magnitude asperities
is another possibilities the these wear debris come between the interphase and that will
increase the coefficient of friction. So, if I start again we say that initially
two, as two body ploughing effect will be there subsequent to that there will be rupture
of asperities wear debris will be at the interphase. There will be adhesion and increase in adhesion
coefficient of friction because more and more asperities are coming into contact. So, there
will be overall dynamics, few asperities will be ruptured. So, ploughing a fracture reduce
few asperities more number of asperities will come in contact. Then adhesion coefficient
will increase and few debris will come at the interphone and coefficient of friction
should increase. That way there is a transition behaviour if I try to plot it.
So, ploughing effect initially I am showing going down with the rupture of asperities.
After that it is reaching to the one dynamic situation by enlarge giving constant coefficient
of friction. Here even though there is possibility of further rupture of asperities, but, those
asperities there is a possibility that they will remain as a debris between the interphase.
So, two body and three body overall will come to the equilibrium will give a steady value
of coefficient of friction. Coming to the second one; there is a red colour
line. This red colour shows that adhesion will increase with a rupture of asperities
more asperities will come in, will come into contact and there will be more and more junction
formation, but, junction formation and junction rupture will be a continuous process. So,
finally, they have to come to one equilibrium position that is why blue colour line and
red colour line when we average will give us some steady behaviour. However, there is
a problem. If situations are not under control; the speed is increasing suddenly, load is
increasing suddenly then any of this line can terminate the component life any of this
line will and the life of a component or which causes excess very high coefficient of friction.
So, that is why we are keeping this as imaginary lines. They depend on the load condition,
they depend on the temperature, they depend on whether the lubricant layer was initially
there and got was removed from the surface because of the starvation, because of pump
failure, because of miss alignment or some other reasons. So, there is a possibility
of this kind of hypothetical lines. It can be may be say similar to pairs. One pair can
show life is starting coefficient of friction is decreasing, reaching in the steady state
condition and then again coefficient of friction increasing at the component or similar component
or similar material pair and at that condition you can show reaching to this condition moving
to straight condition and finally, ends with this line.
Depends on environmental condition this line will be selected or there is a possibility
or extended life or many times we get the infinite life. There is also possibility of
infinite life. It will show coefficient of friction as a steady value throughout this
life there is a possibility. We have been discussing about the sliding friction but
there is another option what we call the rolling friction. From history we know very well that
rolling friction is always preferred compared to sliding friction. What we say, as far as
possible avoid sliding friction. Bring rolling friction into picture. You have heard about
the sliding bearings are been replaced with the small small balls.
So, the coefficient of friction is steady and gives reliably low value and we can say
coefficient of friction due to rolling that is represented here with a mu r is generally
smaller than that caused by the sliding action. This is always desirable for machines. If
I have choice I will prefer rolling friction compared to sliding friction if friction reduction
is my main aim. So, that it can be defined as a ratio of forces also or it can be defined
as a ratio of movements also. In this case we are assuming as a ratio of force the force
required to maintain steady rolling divide by the load which is applied on the roller
or tribe pair. One of the interesting thing is that rolling
coefficient or rolling friction coefficient depends on the hardness. So, there is a symmetry,
there is a similar behaviour. Sliding friction also depends on hardness higher the hardness
by enlarge higher the hardness; coefficient of friction will be lesser. Same behaviour
is adopted or opted by the rolling coefficient of friction also higher the hardness lesser
will be the coefficient of friction and reason behind this is that there is high hardness
there is a lesser chance of what we say that magnitude of deformation will be lesser. Death
or penetration will be lesser in that case. So, if the death or penetration is lesser;
there is a chance that material will show lesser stresses. If I think from stresses
loop point of you from the loading and unloading point of you if materials have stresses behaviour,
it does not regain its position without losing energy then coefficient of friction will be
high. However, it gains the same position without losing much energy then coefficient
of friction will be lesser. We have a couple of example we say that if we start with a
hard steel roller or steel ball also, then if it is roll or on a flat surface or in convex
or concave surface the coefficient of friction may be in the range of .01 to .001.
We are using the word here smooth; that means, surface roughness is not accounted. If the
surface softness accounts then there will be surely some sliding on that. It will not
be perfect rolling. And we are talking about the hardness. If the surface is hard, if the
surface will turn out to be soft then there will be excessive deformation and due to that
excessive deformation there will be loss due to and that will be counted as coefficient
of friction. That is why in second line it is written a roller or sphere or the ball
over here made of a soft material when rolled over other soft surface intended high level
of coefficient of friction or rolling friction will be high. So, even resistance will be
high in that case if the material pair is soft and strong.
If the hard material is a rolling over the hard material deformation will be lower. In
that case coefficient of friction will also be lower. If I see the all mechanisms I can
divide this coefficient of friction due to four mechanisms. We say that even under rolling
condition there is a possibility of micro slip. Micro slip between the material pair,
there is a possibility of elastic deformation, there is a possibility of plastic deformation
and if there is a thermal change or behaviour change due to the temperature then again there
will be coefficient of friction; so, four mechanisms.
But, we are assuming for time being that we are not going in a plastic domain. The plastic
domain coefficient of friction is neglected in this case and there is a very low chance
of micro slip, very low chance of excess of heating.
So, we will consider only the elastic case surface. Elastic itself is going to give coefficient
of friction. So, to demonstrate that, there is diagram which shows that the roller rolling
in clockwise direction. When it start rolling what it will be what happen to the material
it will be going to the some pressure and if there is a rubber material then there will
excess deformation of surface. Now, what will happen if the surface is not
straight, it is going under deformation? That means, a point contact is converting getting
converted to the area contact or line contact is getting converted to the area contact.
So, there is a substantial area of area contact in that that introduces some sort of micro
slip then the as well as the stresses losses. In this case it is shown when it is relief
at the backend if the recovered energy whatever has been given initially it has been recovered
at the backside. But, due to rubber which has heat dissipation capabilities or heat
absorption and capabilities or energy of the absorption capabilities; in that case energy
will not be given back completely as some portion will be lost and that will cause a
coefficient of friction. Now, if I think from the lubricant point of
you we are able to save the use of lubricant does not help to reduce rolling friction.
In this case even when we are providing a lubricant. It does not help much there is
no adhesion it is only the deformation and we know very well liquid by enlarge if it
is very thin lubricant layer it will not completely separating then it will not change coefficient
of friction, it will not absorb any deformation and the load which we are talking in the rolling
contact generally very high compared to sliding contact. In that case lubricant layer really
does not play much role if only elastic deformation is causing coefficient of friction.
So, this is what we will mention here hard steel rolling over soft rubber. That it rolls
along the ball displaced rubber elastic plastically around. If I assume only elastic deformation
then it will regain perfect shape. However, assume elastic plastic then there will be
permanent deformation on the rubber material. For simplicity we generally assume load applied
load is much lower than which can cause a plastic deformation. Now, depends on behaviour
of the material whether it is a bouncy rubber. If it is a bouncy rubber it is not a soggy
rubber, it is not going under plastic deformation what we say that apply load in such a manner
it retains a bounce space on the rubber then coefficient of friction will be lesser.
However the soggy rubber which does not have a good molecular bounding and when it is subjected
to deformation it gets that shape and if it is getting that shape the coefficient of friction
will be high. They will not be energy returned back to the surface. So, we can say that deformation
of material will decide the magnitude of rolling friction whether coefficient of friction will
be high, coefficient of friction will be low that will can be decided by the material behaviour.
If the material is made of good rubber or we say that rubber is made of the good ingredient.
In that case coefficient of friction will be slightly lower compared to the simple period
time rubbers. And again the line is coming out here we say
lubricant cannot reduce deformation of the surface. Therefore, lubricants have very little
effect on the rolling friction. It will not be able to reduce coefficient of friction
substantially at case.
Now, we have number of expressions for the rolling element bearings or which define the,
what will be the rolling friction. We will be discussing those detailed expressions when
we deliver lecture or we discuss about the rolling element behaviours or rolling element
bearing design and selection of the rolling element bearings that time will be discussing
those detail expression. However, I am just providing the two simple
examples in on this slide is that ball bearing we are assuming they are made of the hardest
steel. They are made intentionally with the hardest steel. So, the deformation is negligible.
It can really roll harder, roll to sliding ratio is very very high. Now second assumption
here we are seeing that which load which is applied is within elastic limits. It is not
high enough to produce any plastic flow of the ball. There is no plastic deformation.
What will happen in that case? If this is the situation with which we are providing,
the hysteresis losses will be very low generally lesser than one percent. So, what will happen
most of the cases? The coefficient of friction will be .01 to .001.
However, we know the rolling element bearings who have come through the cages, separators.
We provide cage to separate the two rolling elements. Reason being if the one rolling
element is disturbing other rolling element what we call the fully compliment bearings
load carrying capacities will increase. But, there will be chances of more friction due
to the rolling between two surfaces itself. It will start retarding each other motion
and then it will get a high coefficient of friction at the interphase.
However to get a more uniform loading in that case, we are or we say that to keep separation
between the rolling element, we provide a separator or cages and they have a much more
area of contact with the rolling element. That is causing higher coefficient of friction
at rolling element bearings. When sliding happens between the cage and the ball it will
not be perfectly rolling, it will not be pure rolling, it will be rolling *** sliding then
coefficient of friction naturally will be high. And if we do not provide any lubricant
then coefficient of friction will be really high .2 to .3.
Here, we can say rolling and lubricant is playing a role because there is a sliding
between the cage and rolling element providing lubricant has a meaning. It is a meaningful
to reduce the coefficient of friction due to sliding. But, rolling lubricant otherwise
cannot reduce the coefficient of friction due to perfect rolling or which is happening
due to the elastic deformation and regaining it. The deformation, the only the rolling
element play the deformation. Then lubricant cannot be used or we say that even if it is
used it is going to create some churning lose it will be on the negative side. It will not
give any benefit to us, but, it will give only drawbacks to us. First is that high cost
of the lubricant then again churning losses and then displacing from the contacting pair
which will happens is own. That is they will not be very clean surface. Lubricant cost
as well as churning losses high friction losses. So, we are providing lubricant in the rolling
elements where does only elastic deformation and pure rolling will cause more problem compared
to providing no lubricant or under deforming them under no lubrication conditions. So,
we can say in short; whenever we are choosing lubricant we choose we need to see what kind
of deformation mechanisms or whether the rolling or sliding is happening. If we are able to
quantify sliding ratio if your able to say yeah sliding is thirty percent or sliding
is fifty percent; then there is a meaning to provide lubricant otherwise not. So, is
generally stated because otherwise when we see the definition or the friction we say
that we require third substance to reduce coefficient of friction. While in this case
third substance will create a more coefficient of friction.
So, providing more lubricant in that situation will be more problematic. So, we need to avoid
that kind of situations. So, when we compare rolling element, rolling friction and sliding
friction again I can say that we should always vote for the rolling friction as far as possible.
However, there is a possibility of high stress concentration due to the rolling action which
requires the special treatment of the material may be many times it turns out to be the costly
compared to the simple sliding pair. Sliding pair will be economy economic and we required
a short life or we required we are not caring about the friction loss or gear loss, we can
go ahead the sliding pair. But, if we require d very high reliability definite life, definite
fatigue life with high reliability that in that case we should prefer the rolling element
or we should prefer the rolling friction compared to sliding friction.
In when we discuss the rolling friction; we are adding one more thing that when we take
an example of tire. Then we need to see whether the tire is completely filled with air or
not. When we drive car many times due to the lesser filling in filling of the tire, deformation
of the tire will be excessive and that will cause high coefficient of friction, will lose
will be losing that the petrol consumption or we say that when we travelling some kilometres
per unit litre that will be lesser than tire having completely filled air or we say is
completely filled air. That is why it is this slide show that in free rolling the tire is
deformed or it meets the road surface. But, it recovers as it leaves it is deformed because
of the nature of surface it is a rubber material and is filled with the air. So, it will deform
to some extent, but, it will recover. If we use a good tire material which has a
low stresses analysis, low stresses then energy saving will be very high. We say that if there
is a negligible slip between the tire and the road then energy loss will not be very
large. That is roughly the estimation is given as the coefficient of friction of .01 to .03.
However, if the rubber material is made or we say that tire is made of a rubber material
having high stresses losses what will happen in that case? Elastic deformation will be
very high. More than what we understand when the coefficient of friction was .01 to .03.
Then in that case the rolling friction will be larger and power losses will be higher
side. So, even when we choose next time that tire
for our car we should choose rubber tire which has lesser stresses. However, choosing that
kind of a tire may create some problem what we say when hysteresis losses are lower is
a perfect rolling then there will be some problem related to the steering of the vehicle.
We say that high stress loss per tire increase the controllability. Slight deformation of
the tire will help in controllability, will provide the right direction. But, if it is
a perfect rolling then in that case we face some steering related problem or direction
related problem. So, there should be a trade off. We should not have perfect rolling; there
should be some deformation of the surface. So, that we have a good control on our vehicle
So, this is what we say that controllability means a better griping of the road during
acceleration, deceleration or when we are taking any turn. That is required and in addition
to that this deformation provides some sort of comfort. It acts like a spring action or
maybe say that the part of a shock absorber. It is in does not transmit the odd all road
unevenness to the passengers. So, from that angle, from comfort point of view we can that
some elastic deformation needs to be there or rubber material need to have that kind
of a deformation. It should not be very rigid it should not very solid otherwise the whole
vibration of road whatever the road condition will directly get transmitted to the passenger
who is sitting inside and it will not be very good option.
So, a balance to keep a low coefficient of friction there should be perfect rolling.
To give good controllability good comfort there should be some good elastic deformation
and whenever there is some elastic deformation, surely there will be some additional sliding
or micro slip will be there and coefficient of friction even under rolling due to deformation
will be high compared to perfect shape will be non deformation or we say rigid tire coefficient
of friction. With this I am closing today’s lecture and
will be starting with related to friction instability, friction causes on instability
in number of machines. We will be discussing in our next lecture. Thank you.